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Chapter 2: Problem 84

Simplify each expression. $$ 6\left(\frac{t}{6}\right) $$

Short Answer

Expert verified
The simplified expression is \(t\).

Step by step solution

01

Identify the Expression

The given expression is \(6\left(\frac{t}{6}\right)\).
02

Apply the Distributive Property

Notice that the term \(6\) outside the parentheses can be simplified with the term \(6\) in the denominator inside the parentheses.
03

Simplify the Fraction

Simplify \(6\left(\frac{t}{6}\right)\) by canceling out the 6's: \(6 \times \frac{t}{6} = t\).
04

Final Simplified Expression

After simplifying, the final expression is \(t\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
The distributive property allows us to simplify expressions by distributing a factor across terms inside parentheses. In algebra, it is written as: \(\text{a}(b + c) = ab + ac\). This rule also applies to subtraction and variables. For instance, \(5(x - 2) = 5x - 10\). The distributive property is useful for making complex expressions easier to work with.
Fraction Simplification
Fraction simplification reduces fractions to their simplest form. To simplify \(\frac{t}{6}\) and then multiply by 6, we can cancel the common factors. In the given exercise, we have: \(6\frac{t}{6}\). Cancel the 6's to get the simplified result: \(t\). This makes calculations easier and expressions cleaner.
Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operators (such as +, -, \, \, and /). Simplifying these expressions involves several steps:
  • Combine like terms.
  • Use the distributive property.
  • Simplify fractions.
The final goal is to rewrite the expression in the simplest form. This helps in solving equations or finding function values more efficiently. In the exercise, simplifying \(6\frac{t}{6}\) led us directly to the simplest form: \(t\). This is an example of breaking down a complex expression into something more manageable.

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Most popular questions from this chapter

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